Approximations for weighted bootstrap processes with an application

✍ Scribed by Lajos Horváth; Piotr Kokoszka; Josef Steinebach

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 175 KB
• Volume: 48
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(99)00190-x

✦ Synopsis

Let ÿn(t) denote the weighted (smooth) bootstrap process of an empirical process. We show that the order of the best Gaussian approximation for ÿn(t) is n -1=2 log n and we construct a sequence of approximating Brownian bridges achieving this rate. We also obtain an approximation for ÿn(t) using a suitably chosen Kiefer process. The result is applied to detect a possible change in the distribution of independent observations.